Unveiling radio halos in galaxy clusters in the LOFAR era

Giant radio halos are mega-parsec scale synchrotron sources detected in a fraction of massive and merging galaxy clusters. Radio halos provide one of the most important pieces of evidence for non-thermal components in large scale structure. Statistics of their properties can be used to discriminate among various models for their origin. Therefore, theoretical predictions of the occurrence of radio halos are important as several new radio telescopes are about to begin to survey the sky at low frequencies with unprecedented sensitivity. In this paper we carry out Monte Carlo simulations to model the formation and evolution of radio halos in a cosmological framework. We extend previous works on the statistical properties of radio halos in the context of the turbulent re-acceleration model. First we compute the fraction of galaxy clusters that show radio halos and derive the luminosity function of radio halos. Then, we derive differential and integrated number count distributions of radio halos at low radio frequencies with the main goal to explore the potential of the upcoming LOFAR surveys. By restricting to the case of clusters at redshifts <0.6, we find that the planned LOFAR all sky survey at 120 MHz is expected to detect about 350 giant radio halos. About half of these halos have spectral indices larger than 1.9 and substantially brighten at lower frequencies. If detected they will allow for a confirmation that turbulence accelerates the emitting particles. We expect that also commissioning surveys, such as MSSS, have the potential to detect about 60 radio halos in clusters of the ROSAT Brightest Cluster Sample and its extension (eBCS). These surveys will allow us to constrain how the rate of formation of radio halos in these clusters depends on cluster mass.